Napoli are second in Serie A after Italy forward Lorenzo Insigne scored twice to help his side win at Torino.
The 27-year-old rifled home the first inside the opening five minutes before Simone Verdi doubled the lead after being set up by Dries Mertens.
Torino scored through Andrea Belotti's penalty before Insigne made it 3-1 with a shot in off the post.
Napoli have won four of their first five league games under former Chelsea boss Carlo Ancelotti.
They entertain mid-table Parma on Wednesday (20:00 BST) before travelling to meet leaders Juventus next Saturday (17:00 BST).
Ancelotti's side are at home to Liverpool in the Champions League on 3 October (20:00 BST).
Roma's poor start to the season continued with a 2-0 defeat at Bologna.
Goals either side of half-time by Federico Mattiello and Federico Santander left the Rome club with just one win in six league and cup games.
Sunday's result followed a 3-0 defeat at European champions Real Madrid last Wednesday in the Champions League.
Last season's Champions League semi-finalists have five points from five Serie A games and are just one point above Bologna, who sit in the relegation zone.
Roma host Lazio in the Rome derby next Saturday (14:00 BST).
Roma's fans saw their team fall to a second away defeat in five days
Unlike neighbours Roma, Lazio are in fine form after hammering Genoa 4-1 - their fourth successive win.
Former Genoa striker Ciro Immobile scored twice against his former club, while ex-Manchester City forward Felipe Caicedo and Sergej Milinkovic-Savic got the other two.
Genoa's goal came from Poland forward Krzysztof Piatek.
While Roma entertain Frosinone on Wednesday (20:00 BST) before next weekend's Derby della Capitale, Lazio are at Udinese (18:00 BST) on the same night.
Ciro Immobile has scored four goals in his past three Serie A games against Genoa